Another example (more common with me) is marking the wrong site for off-topic...
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Nicholas RileyFeb 20 '11 at 2:01

Pay more attention to what you are doing, are you sure you want to format your computer? Please note that one close reason that was off doesn't matter, it does contribute to the 5 close votes and the majority will choose the right close vote reason anyway...
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Tom WijsmanNov 4 '11 at 18:16

1

Tom. My lack of motor skills is not the same as not paying attention.
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toolkitJul 27 '12 at 19:50

@DannyBeckett this is however implemented other as the OP would wish (not possible to change the vote, only retract) so it's an independent feature request.
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ВГДЕЖЅZЗИІКЛМНОПҀРСТȢѸФХJan 31 '14 at 9:44

Given the recent changes to voting that allow users to retract their own votes, I think the next logical step is to consider implementing this feature.

Generally speaking, I see 3 cases where one might want to change a voting reason

Mis-click - typos happen and a user clicks the wrong radio button before clicking "close" (as the example in the question shows)

Misreading of the question - you see this happen frequently, someone reads the question one way, votes to close, and then rereads a question and sees the original reason is not applicable, but another reason is better.

The question changes - through comments and editing, the OP changes the question so the original reason isn't valid, but a different reason is more applicable

The 3rd point is the main reason why I think this feature would be valuable, and a big reason why is because of all of the effort that has been put into revamping the close system in the recent months. We wanted the close/on-hold reasons to provide as much useful information to the OP as possible, but how useful is it when the reason is wrong?

Ideally, the close reason would be dynamic and allow someone to change their reason up to the point that the question gets reopened, to allow for editing that doesn't quite fix the post but changes the reason why it is closed. But at a minimum, at least allow a close voter to change his vote up until the question is closed.

This really needs to happen. Probably once a day I realize that my reason for voting to close a question was wrong, or at least not the best reason, but there is no way to fix my error.

There should be a window of time during which I can modify my reason and/or retract my vote while retaining the option to vote to close again, just like the way voting up and down works. As it is, if I pick a bad reason or if the question changes after I voted to close, my only options are leave it as-is, with an incorrect reason, or retract my close vote entirely even if I still think the question should be closed.

Obviously, if the question is already closed, the vote should be finalized/locked, and I should have to vote to reopen. But until then, I should be able to change my reason, at least one time.